Initial investigations of spectral methods for numerical plasma kinetic theory

Summary form only given. A spectral element code based on polynomial collocation at the Gauss-Radau-Legendre points within each phase space element has been developed. This code has been used to test a variety of explicit and implicit time stepping schemes, and the numerical tests show excellent conservation for modest numbers of unknowns (for example, 10/sup -2%/ change in the total number of particles after 100,000 time steps of only 1500 unknowns). These methods do not suffer from any dispersion or dissipation of delicate phase space structures such as trapped particle distributions. The time stepping methods tested so far (modified Euler, Adams-Bashforth and a semiimplicit splitting method) have the property of damping unresolved scales and thereby suppressing phase space filamentation, the bane of collisionless plasma kinetics codes.